Correlation functions of Ising spins on thin graphs

TL;DR

This paper analyzes the correlation functions of an Ising spin model on random graphs derived from $$ field theory, combining analytical calculations with numerical simulations to understand phase transition behaviors.

Contribution

It provides explicit calculations of correlation functions in both symmetry phases for the Ising model on thin graphs, validated by Monte Carlo simulations.

Findings

Correlation functions match between analytical and numerical results.

The model exhibits a mean field phase transition.

Explicit formulas for correlation functions in large volume limit.

Abstract

We investigate analytically and numerically an Ising spin model with ferromagnetic coupling defined on random graphs corresponding to Feynman diagrams of a $\phi^q$ field theory, which exhibits a mean field phase transition. We explicitly calculate the correlation functions both in the symmetric and in the broken symmetry phase in the large volume limit. They agree with the results for finite size systems obtained from Monte Carlo simulations.